Related papers: Two-parametric PT-symmetric quartic family
We construct supersymmetric quantum mechanics in terms of two real supercharges on noncommutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two and three dimensional noncommutative superoscillators. We further…
We constuct a family of hemisystems of the parabolic quadric $\mathcal{Q}(2d, q)$, for all ranks $d \ge 2$ and all odd prime powers $q$, that admit $\Omega_3(q) \cong \mathrm{PSL}_2(q)$. This yields the first known construction for $d \ge…
We reflect real spectra of new logarithmic model PT-symmetry operators with singular and non-singular in nature. We also notice that iso-spectral nature between inverted and non-inverted logarithmic PT-symmetric potentials. Present…
If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly…
We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients of the canonical coherent states by a specific generalized factorial depending on a parameter gamma. These states are superposition…
A theorem of E.Lerman and S.Tolman, generalizing a result of T.Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a positive integer label attached to each of their facets. In…
The location of the zeros of a two-parameter family of complex-valued harmonic quadrinomials depends on the parameters. In this paper, we determine and demonstrate that the image of some critical circle under these two-parameter family of…
The domain ${\cal D}$ of all the coupling strengths compatible with the reality of the energies is studied for a family of non-Hermitian $N$ by $N$ matrix Hamiltonians $H^{(N)}$ with tridiagonal and ${\cal PT}-$symmetric structure. At all…
We study a reflectionless PT-symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the…
In this work, we delve into the theory of sheared potentials in non-relativistic quantum mechanics. After defining what we mean by a family of sheared potentials, we consider these families in two particular but emblematic cases, the…
The goal of the paper is to investigate the dynamics of the eigenvalues of the Sturm-Liouville operator with summable PT-symmetric potential on the finite interval. It turns out that the case of a complex Airy operator presents an exactly…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…
Three-parametric family of non-Hermitian but ${\cal PT}-$symmetric six-by-six matrix Hamiltonians $H^{(6)}(x,y,z)$ is considered. The ${\cal PT}-$symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies…
In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^\epsilon of the harmonic oscillator Hamiltonian, where \epsilon is a real parameter. These complex Hamiltonians, possessing PT…
We study orthogonal polynomials on a fully symmetric planar domain $\Omega$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $\Omega$, we show that orthogonal polynomials that are even in…
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere $S^2$ is proved. A classification of these families up to moderate equivalence in neighborhoods of their large…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…
We consider general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$. A distribution matrix-valued function $\Si(s), \; s\in\bR,$ is called a…